In this letter, a construction of asymmetric Gaussian integer zero correlation zone (ZCZ) sequence sets is presented based on interleaving and filtering. The proposed approach can provide optimal or almost optimal single Gaussian integer ZCZ sequence sets. In addition, arbitrary two sequences from different sets have inter-set zero cross-correlation zone (ZCCZ). The resultant sequence sets can be used in the multi-cell QS-CDMA system to reduce the inter-cell interference and increase the transmission data.

The present paper introduces a novel type of structured ternary sequences having a zero-correlation zone (zcz) for both periodic and aperiodic correlation functions. The cross-correlation function and the side lobe of the auto-correlation function of the proposed sequence set are zero for phase shifts within the zcz. The proposed zcz sequence set can be generated from an arbitrary pair of an Hadamard matrix of order lh and a binary/ternary perfect sequence of length lp. The sequence set of order 0 is identical to the r-th row of the Hadamard matrix. For m ≥ 0, the sequence set of order (m+1) is constructed from the sequence set of order m by sequence concatenation and interleaving. The sequence set has lp subsets of size 2lh. The periodic correlation function and the aperiodic correlation function of the proposed sequence set have a zcz from -(2m+1-1) to 2m+1-1. The periodic correlation function and the aperiodic correlation function of the sequences of the i-th subset and k-th subset have a zcz from -2m+2-(lh+1)((j-k) mod lp) to -2m+2-(lh+1)((j-k) mod lp). The proposed sequence is suitable for a heterogeneous wireless network, which is one of the candidates for the fifth-generation mobile networks.

The present paper proposes two new methods for constructing polyphase asymmetric zero-correlation zone (A-ZCZ) sequence sets. In previous studies, the authors proposed methods for constructing quasi-optimal polyphase A-ZCZ sequence sets using perfect sequences and for constructing optimal polyphase A-ZCZ sequence sets using discrete Fourier transform (DFT) matrices. However, in these methods, the total number of sequences in an A-ZCZ sequence set cannot exceed the period of the perfect sequence or the dimension of the DFT matrix used for constructing the A-ZCZ sequence set. We now propose two extended versions of these methods. The proposed methods can generate a quasi-optimal or optimal polyphase A-ZCZ sequence set where the total number of sequences exceeds the period of the perfect sequence or the dimension of the DFT matrix. In other words, the proposed methods can generate new A-ZCZ sequence sets that cannot be obtained from the known methods.

Recently, asymmetric zero-correlation zone (A-ZCZ) sequence sets that are composed of several sequence subsets have been proposed. In A-ZCZ sequence sets, the zero-cross-correlation zone (ZCCZ) length between different sequence subsets is larger than the zero-correlation zone (ZCZ) length in each sequence subset. However, the ZCCZ length between different sequence subsets was not precisely shown in previous studies. The present letter shows precisely the ZCCZ length between different sequence subsets. This information is useful for estimating the magnitude of inter-cell interference when designing approximately synchronized code-division multiple-access (AS-CDMA) systems.

The present paper proposes a new method for constructing polyphase asymmetric zero-correlation zone (A-ZCZ) sequence sets. The proposed method can generate A-ZCZ sequence sets that cannot be obtained from methods proposed by other researchers and is a generalized version of our previously proposed method. An A-ZCZ sequence set can be regarded as a ZCZ sequence set. The newly obtained A-ZCZ sequence sets include quasi-optimal ZCZ sequence sets of which the zero-cross-correlation zone (ZCCZ) length between different sequence subsets is larger than the mathematical upper bound of conventional ZCZ sequence sets. A new method for extending the A-ZCZ sequence sets is also presented in the present paper.